Fast transform based preconditioners for 2D finite-difference frequency-domain – Waveguides and periodic structures

The fields scattered by dielectric objects placed inside parallel-plate waveguides and periodic structures in two dimensions may efficiently be computed via a finite-difference frequency-domain (FDFD) method. This involves large, sparse linear systems of equations that may be solved using preconditioned Krylov subspace methods. Our preconditioners involve fast discrete trigonometric transforms and are based on a physical approximation. Simulations show significant gain in terms of computation time and iteration count in comparison with results obtained with preconditioners based on incomplete LU (ILU) factorization. Moreover, with the new preconditioners, the required number of iterations is independent of the grid size.